Set the Instant Pot to the “Sauté (More)” setting. Once it is hot, add the vegetable oil.
Season the pork with 2 tablespoons kosher salt and 1 teaspoon pepper. Brown the pork shoulder in the Instant Pot, searing it on all sides. (If needed, do this in batches to avoid overcrowding the pot.)
Add all of the browned pork shoulder, plus any juices, to the Instant Pot.
Add the chopped onion, garlic, orange juice, lime juice, chili powder, oregano, cumin, coriander and chicken stock to the Instant Pot.
Set it on the “Pressure Cook” setting for 90 minutes and close the lid.
Once the pork is done cooking, transfer it to a cutting board, and using two forks, shred it into pieces and serve it with Cherry Tomato Pico de Gallo Salsa.